Almost. The word 'who' doesn't work as the subject. Here are some suggestions:
"He who learns another language, acquires another soul"
This sounds elegant, but is a little old-fashioned and rather sexist/male-orientated. Other possibilities are:
'Anyone who learns another language, acquires another soul"
"A person who learns another language, acquires another soul"
"Whoever learns another language, acquires another soul"